In the late 80s we were flying to Paris from somewhere. I was about 7 or 8 at the time so details are sketchy, but I do remember thinking that ILS would see us through (I was "reading" aviation books since from the age of 3 or 4).
We had been in a holding pattern for ages (40 mins according to mum, I remember seeing sunlight rotating through cabin many times) due to fog in Paris. Eventually we went down for what I assume was a CATIII landing. My mum reckons that you couldn't see the wings but lets just take that as meaning really bad fog.
As evidenced by the long silence during descent and approach, the pax were not too comfortable with landing in such poor visibility. We made a smooth touchdown and the cabin erupted into applause.
However, the pilot then informed us that he couldn't find the way back to the gate due to the fog. So I guess that makes it pretty thick.
I think that situation was a bit more worthy of applause than most.
It probably just takes a few silly passengers to start clapping and then the rest will follow so that they don't look like b***ards.